Larmor precision frequency

When the interaction frequency resonance transitions other than the principal one, Vi —Vi are generally difficult to observe. In such a situation the value of e2qQ is obtained from the splitting of the principal transition. The values of e2qQ obtained as a function of temperature are plotted in Fig. 2.7. 

In order to better illustrate these points, consider, for example, a magnet such as the one described in Section III.D. It reaches the maximum field of 1.143 T, corresponding to 48.7 MHz of Larmor frequency, with a current of 400 A. It follows that for a very low magnetic field corresponding to, let us say, 1 kHz, one has to set a current of just 8 mA. In order to do that, one should be able to control the current with a precision and resolution of about 20 ppm of the maximum value. The required absolute precision is therefore of the same order of magnitude as the current offsets and thermal drifts of even the best analog electronic components. 

The issues with respect to obtaining chemical information within an imaging experiment are considered next. The description of image acquisition given in Section II.A.l was based on the assumption that the Larmor frequency of a nuclear spin is directly related to its location in the sample, as determined by the applied magnetic field gradient. As discussed by Callaghan (13), this is precisely true only... 

We can look at this more precisely using the product operator formalism, even though it is more important to focus on the conceptual picture rather than the math. For a resonance with Larmor frequency vG, we have during the first gradient... 

A second improvement was that we measured the cyclotron frequency in the precision trap simultaneously with the Larmor frequency. This reduces to a large extent possible errors induced by a temporal variation of the magnetic field which occurs in superconducting solenoids typically at a level of 10-8 per hour. In the final experiment we measure the rate of spin Hips at different ratios of the Larmor- and cyclotron field frequencies. An example is shown in Fig. 10. The linewidth is of the order of 10-8 and the g factor can be determined with a statistical uncertainty below 1 ppb [19]. 

Fig. 10. Example of a Larmor resonance in the precision trap. Here the spin flip probability is plotted versus the ratio g = 2ui L/u)ec of the microwave excitation frequency (jj L and the electron s free space cyclotron frequency ui%. This is convenient because this ratio is independent of the magnetic field...

Comparison of theory to precision experiment often involves some other experimental data from different fields. In particular, the g factor experiment [1] deals with a comparison of two frequencies the Larmor spin precession frequency... 

This approach is similar to the use of the field variation of the centre of gravity of the MAS centreband, but has the advantage that the narrower, more symmetric line makes determination of the correct position of the centre of gravity more precise. For experiments carried out at two magnetic fields where the Larmor frequencies are voi and vo2 for the measured DOR peak positions (in ppm) at the two magnetic fields of 8dori,2 then... 

As was discussed in section 2.3, the Larmor frequency is a signed quantity and is negative for nuclei with a positive gyromagnetic ratio. This means that for such spins the precession frequency is negative, which is precisely what is shown in Fig. 3.2. 

Let us imagine that the frame of reference is not static but is rotating clockwise around the z axis at the carrier frequency vx. In Figure 4.7b, we are looking down the z axis toward the xy plane and place the vx vector on the x axis, where it apparently remains even though it is really precessing at the carrier frequency of, say, 300 MHz. The two faster Larmor vectors (vLl and vl 2) appear to precess clockwise, whereas the slowest vector (vl3) appears to precess counterclockwise, that is, at their difference frequencies 2000 Hz, 800 Hz, and (—) 1000 Hz—precisely those used to produce the FID. 

Variable frequency proton Ti studies were first used to detect the characteristic dependence of Ti due to director fluctuations [6.20] in liquid crystals. It was recognized soon after that besides the director fluctuations, relaxation mechanisms, which are effective in normal liquids such as translational self-diffusion and molecular reorientation [6.24], also contribute to the proton spin relaxation in liquid crystals. Though the frequency dependences of these latter mechanisms are different from the relaxation, the precise nature of proton Ti frequency dispersion studied over a limited frequency range using commercial NMR spectrometers often may not be unambiguously identified. Furthermore, because of a large number of particles involved in collective motions, the motional spectrum has much of its intensities in the low-frequency domain far from the conventional Larmor frequencies. The suppression of director fluctuations in the MHz region due... 

Figure 2 Precision of the initial stabilization of the evolution field. The plot represents the voltage transient recorded with a Hall probe (6 iJ.T/mV) and a 16 bit analogue-to-digital converter. The field level corresponds to a proton Larmor frequency of 3.5 kHz. The fieldcycling relaxometer is described below. This plot demonstrates that the evolution field can be stabilized within 1 digital unit in a ring-down time less than 1 ms.

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